How do you get the cigar smell out of cigar boxes?

You might try leaving the humidor open for a long time... months. Then give the wood a light sanding and close the box for a couple of weeks with a humidification source. See if you detect a odor. If so, you will have to use the box for another purpose. The problem is the cedar inside the humidor is porous and designed to absorb from it's surroundings. With the prices the way they are, You need the best storage device available to you.

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You really CAN'T remove the burnt cigar smell. If you like saving half-smoked cigars to finish at another time, get a new humidor for unsmoked cigars, and use this one for the half-smoked ones.